A threshold logic element is defined as an n-input processing element having an output defined as:
                                          f            T                    ⁡                      (            X            )                          =                  {                                                                      1                  ,                                                                                                  if                    ⁢                                                                                  ⁢                                                                  ∑                                                  i                          =                          1                                                n                                            ⁢                                                                        w                          i                                                ⁢                                                  x                          i                                                                                                      ≥                  T                                                                                                      0                  ,                                                            Otherwise                                                                        (        1        )                                                      f            T                    ⁡                      (            X            )                          =                  {                                                                      1                  ,                                                                                                  if                    ⁢                                                                                  ⁢                                                                  ∑                                                  i                          =                          1                                                n                                            ⁢                                                                        w                          i                                                ⁢                                                  x                          i                                                                                                      ≤                  T                                                                                                      0                  ,                                                            Otherwise                                                                        (        2        )                                                      f            T                    ⁡                      (            X            )                          =                  {                                                                      0                  ,                                                                                                  if                    ⁢                                                                                  ⁢                                                                  ∑                                                  i                          =                          1                                                n                                            ⁢                                                                        w                          i                                                ⁢                                                  x                          i                                                                                                      ≥                  T                                                                                                      1                  ,                                                            Otherwise                                                                        (        3        )                                                      f            T                    ⁡                      (            X            )                          =                  {                                                                      0                  ,                                                                                                  if                    ⁢                                                                                  ⁢                                                                  ∑                                                  i                          =                          1                                                n                                            ⁢                                                                        w                          i                                                ⁢                                                  x                          i                                                                                                      ≤                  T                                                                                                      1                  ,                                                            Otherwise                                                                        (        4        )            
where X=[x0, x1, . . . , xn-1], W=[w0, w1, . . . , wn-1], and T are a set of data inputs that represent Boolean variables, a set of fixed signed integer weights associated with data inputs, and a threshold value, respectively. A threshold logic element may be used to implement a threshold logic function as described by one of the equations above, which is equivalent to a complex Boolean function. Threshold logic elements may occupy less room than a Boolean network needed to implement the complex Boolean function. Thus, threshold logic elements may be used in place of Boolean networks to provide the same functionality while consuming less area in an integrated circuit (IC).
Unfortunately, ICs are subject to piracy. Obfuscation techniques have been developed for Boolean networks that prevent a pirate from reverse engineering an IC formed by Boolean networks by hiding the functionality of the threshold logic network. However, obfuscation techniques have not been developed for threshold logic networks. Furthermore, obfuscation techniques developed for Boolean networks significantly increase the power, delay, and area consumed within the IC.